Hannan条件下加权Bernoulli随机场的极限定理
Limit theorems for weighted Bernoulli random fields under Hannan's condition
摘要：
考虑一个满足汉南条件的伯努利随机场。最近，矩形指标集上随机场部分和的不变原理被建立。本文通过研究加权Bernoulli随机场的极限定理，包括任意指标集上部分和的中心极限定理和高斯随机场的不变原理，补充了已有的结果.大多数结果改进了前人关于Bernoulli随机场在吴条件下的结果，比Hannan条件更强。
英文摘要：
Consider a Bernoulli random field satisfying the Hannan's condition. Recently, invariance principles for partial sums of random fields over rectangular index sets are established. In this note we complement previous results by investigating limit theorems for weighted Bernoulli random fields, including central limit theorems for partial sums over arbitrary index sets and invariance principles for Gaussian random fields. Most results improve earlier ones on Bernoulli random fields under Wu's condition, which is stronger than Hannan's condition.
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